System and method for liquid delivery evaluation using solutions with multiple light absorbance spectral features

ABSTRACT

A system and related method for improved liquid delivery evaluation using a solution containing one or more dyes such that the solution exhibits multiple distinct detectable light absorbance spectral features for calibrating or testing over extended volume or dilution ranges are described. The system includes: a photometric instrument capable of measuring optical absorbance at multiple wavelengths; one or more sample solutions to be dispensed using the liquid delivery system whose performance is being tested or calibrated; and vessels optionally pre-filled, or filled by the user, with diluent solution. The sample solutions contain one or more dyes, chosen so that multiple distinct detectable light absorbance spectral features, such as peaks and/or valleys and/or plateaus of the solution can be distinguished for volume or dilution ranges of interest. The concentrations of the dyes may be chosen so that a large volume delivery device is calibrated using a spectral feature in the solution with a low absorbance per unit pathlength, while a small volume delivery device is calibrated with the same sample solution but using a different spectral feature with a high absorbance per unit pathlength.

CROSS REFERENCE TO RELATED APPLICATION

The present invention is related to application Ser. No. 12/098,875,filed on the same date hereof, with the same title and assigned to acommon assignee, now U.S. Pat. No. 7,791,716. The content of thatrelated patent is incorporated herein by reference.

BACKGROUND OF THE INVENTION

1. Field of the Invention

The present invention relates to a system for determining the volume ofa liquid delivery. More particularly, the present invention relates tosystems and related methods to test or calibrate liquid delivery devicesusing a sample solution having multiple distinct detectable lightabsorbance spectral features using one or more dyes to cover a volumerange, or a dilution range, of interest.

2. Description of the Prior Art

All currently manufactured calorimetric systems for testing orcalibrating liquid delivery devices (e.g., the PCS® system and the MVS®system, both offered by Artel, Inc. of Westbrook, Me., assignee of thepresent invention and application, and the Pipette Volume CalibrationKit offered by VistaLab of Mt. Kisco, N.Y.) use a multiplicity of samplesolutions for the purpose of testing a wide range of deliverablesolution volumes. The sample solution is delivered by the device beingtested into a diluent in a measurement vessel, and the solutions aremixed before measuring the absorbance of the resulting mixture. Aconcentrated sample solution is used to test a small liquid deliveryvolume, and a more dilute sample solution is used to test a large liquiddelivery volume. As used herein, a “vessel” is any vial, cell, bottle,microtiter plate or other type of container for retaining a fluidtherein, whether such vessel is sealed or not. Also, the vessel may bedesigned for collecting optical absorbance measurements by use of ahorizontal beam spectrophotometer (such as a conventional UV-Visspectrophotometer like the Cary 5000, Varian, Inc., Palo Alto, Calif.)or a vertical beam spectrophotometer (such as a microtiter plate readerlike the ELx800, BioTek Instruments, Winooski, Vt.).

In simplified terms, the PCS® system includes one or more devices andone or more solutions used to calibrate a single-channel liquiddispensing device. On the other hand, the MVS® system includes one ormore devices and one or more solutions used to calibrate a multi-channelliquid dispensing device. The difference between the two systems relatesto the calculations performed subsequent to conducting absorbancemeasurements at one or more wavelengths corresponding to featurespresent in the spectrum of the solution(s).

In the case of one commercial embodiment of the Artel PCS® system, forexample, four different concentrations of a sample solution, eachtargeting the same spectral feature, are provided to cover the volumerange from 2 microliters (μl) to 5000 μl. Two additional concentrationsof the same sample solution extend the range down to 0.1 μl. The reasonfor using different concentrations is to maintain a measurable signallevel (absorbance change resulting from the delivery of an aliquot ofsample solution or diluent) within a defined signal range over the fullrange of liquid delivery volumes. That is to say, each concentration ofsample solution is manufactured to produce a final measurable absorbancewithin a defined absorbance range for any delivered volume that iswithin the volume range for which the solution is designed. Allconcentrations of sample solution of the PCS® system are designed toproduce measurable absorbance values over the same absorbance range. Thedisadvantage to using a multiplicity of solutions is that the user needsto stock them, rotate stock to make sure that the solutions are withintheir expiration date, and then choose which one or ones to use, and todispense the correct solution(s) into one or more vessels from which thedelivery device can aspirate the correct solution. There is ampleopportunity for error, waste of unused solutions from the vessels, andwaste of time and unnecessary distraction from the job of testing thedelivery device. It is thus desirable to devise a method that wouldreduce the number of sample solutions required to test the entire volumerange that can be delivered by a liquid delivery device.

In addition to volume delivery testing, colorimetric measurement systemsusing multiple concentrations of the same sample solution can be used totest dilution protocols, which are commonly employed in life sciencelaboratories. Such dilution protocols are often employed in drugdiscovery testing where a compound of interest is serially dilutedacross a microtiter plate. For example, the user dispenses 200 μL ofsample solution into the first column of a microtiter plate and thenaspirates 100 μL from that first column and dispenses it into 100 μL ofdiluent in the second column, creating a 1:2 dilution ratio of thesample solution in the second column. Serially repeating this processacross all columns in the plate results in a range of dilutions from a1:1 ratio up to a 1:2048 ratio. An effective dilution protocol system isdescribed in pending U.S. patent application Ser. No. 11/854,594, filedSep. 13, 2007, having as assignee the assignee of the presentapplication. The entire content of the referenced Ser. No. 11/854,594pending application is incorporated herein by reference. If the MVS®system were used to test the dilutions made in this example, five samplesolutions would be needed to cover the entire range of dilution ratiosbecause each sample solution can only test a four- or five-fold range ofdilution ratios before the absorbance signal of the single spectralfeature in the sample solution is too low to be measured by themicrotiter plate reader. Thus, to measure all dilution steps of thisprocess, the serial dilution protocol has to be repeated for each of thefive sample solutions such that a limited range of the dilution ratioseries is tested with each sample solution. That is to say, each of thefive sample solutions is serially diluted using the defined protocol.For each of the sample solutions, only a portion of the produceddilutions will be within a measurable absorbance range, but thecombination of data from all sample solutions will provide measurementsfor every step of the entire process. As a result, many test vessels arefilled with sample solution to cover the entire dilution range ofinterest but only a fraction are actually used. Thus, there is a wasteof solution and of time.

Alternative methods for testing serial dilution protocols includefluorescence, which covers a far greater range (1,000-10,000 foldgreater range) of dilution ratios before the signal is too low tomeasure. However, the fluorescence method introduces variability becauseof the instability of fluorescent dyes due to photo-bleaching,quenching, etc, and also lacks the traceability to internationalstandards of an absorbance-based photometric approach. Therefore, it isalso desirable to devise an absorbance-based photometric method thatwould measure an extended range of dilution ratios using one samplesolution containing multiple spectral features, each capable of testinga unique four or five fold range of dilution ratios as an alternative tofluorimetry testing of dilution processing as noted herein.

Other systems have been described for enhancing calibration accuracy.See, for example, U.S. Pat. No. 5,298,978 for “Pipette CalibrationSystem” of Curtis et al., incorporated herein by reference, U.S. Pat.No. 4,354,376 for “Kit for Calibrating Pipettes” of Greenfield, and U.S.Pat. Nos. 6,741,365 and 7,187,455 for “Photometric Calibration of LiquidVolumes” of Curtis, also incorporated herein by reference. These systemshave limitations resolved by the use in the present invention of a dye,or a plurality of dyes, capable of producing multiple distinctdetectable light absorbance spectral features in a smaller set of samplesolutions, wherein each distinct detectable light absorbance spectralfeature allows calibration or testing over a specific volume range. Adye is any molecule or chemical compound that imparts one or morefeatures to the absorbance spectrum of the solution. This definition isnot intended to limit the feature to the visible region of the spectrum,nor to limit the spectral feature to the dye or dyes alone. The solventcould also impart a spectral feature that could be used as is describedin this invention. One skilled in the art may recognize that a dye maybe the functional equivalent of a chromophore. As used herein, “distinctdetectable light absorbance spectral features” are distinct anddetectable peaks, valleys, plateaus, or any combination of peaks andvalleys and plateaus in the absorbance spectrum of a solution undertest. In the case of U.S. Pat. No. 4,354,376 of Greenfield, there isonly one distinct detectable light absorbance spectral feature. In thecase of U.S. Pat. No. 5,298,978 of Curtis et al., there is a secondfeature present in the spectrum of the diluent solely for the purpose ofdetermining the pathlength of light through the vessel before any samplesolution is added to the vessel, minimizing uncertainty in the resultsdue to uncertainty in vessel dimensions. This second spectral feature isnot contained in the sample solution dispensed with the liquid deliverydevice under test. In the case of U.S. Pat. Nos. 6,741,365 and 7,187,455to Curtis, two spectral features are used to eliminate uncertainty inresults that would otherwise occur due to uncertainty in the volume ofdiluent added to the tapered wells of the microtiter plate used as ameasurement vessel. Both spectral features are contained in the samplesolutions, however the function of the second spectral feature (in thatparticular case, CuCl₂) is to correct for the unknown volume of diluent,not to cover a wider range of dispensing volumes.

What is needed is a system and related method to resolve the limitationsof the existing liquid delivery measurement systems in which the use ofcolorimetric techniques to evaluate liquid delivery devices or protocolsrequires the use of an excess number of sample solutions for volume anddilution ranges of interest.

SUMMARY OF THE INVENTION

The purpose of the present invention is to resolve the above-notedlimitations by simplifying the testing or calibrating of liquid deliverydevices. This greater simplicity will reduce costs, allow users to dotheir work more effectively, and reduce the likelihood of errors. Thisinvention achieves this greater simplicity by reducing the number ofdifferent sample solutions required to test a large range of volumes, ora large range of dilutions, to a minimal number, ideally only one, fromtypically four. The present invention is designed to be in conformancewith International Standards Organization (ISO) standard 8655 part 7and, further, it is designed to provide results traceable tointernational standards, thereby making it advantageous overfluorimetric techniques. Finally, this invention is designed to extendthe testable dilution range or volume range of a sample solution byincreasing the number of spectral features in the sample solution.Specifically, an extended testable volume range enables the use of asingle sample solution, optimally, to cover pipettes (or other relevantdelivery devices) most commonly tested or calibrated in the volume rangeof about 2 μl to about 5000 μl. Similarly, an extended range ofdilutions can be tested using a single sample solution, optimally, for arange of 1:1 up to 1:2500. In the event a single sample solution cannotbe used for a desired volume or dilution range, the present inventionnevertheless enables use of a smaller set of sample solutions than hasheretofore been required.

The present invention is a system and related method for improved liquiddelivery evaluations using solutions containing one or more dyes orother light absorbing compounds or chemicals, which in combination orindividually, exhibit multiple distinct detectable light absorbancespectral features, each solution capable of calibrating or testing overa wide volume range, or dilution range, of interest. The systemincludes: a photometric instrument capable of measuring opticalabsorbance at multiple wavelengths; one or more reagents including oneor more sample solutions to be dispensed using the liquid deliverysystem whose performance is being tested or calibrated; and, optionally,vessels pre-filled with diluent solution. The sample solution containsat least one dye, chosen so that when any volume within a volume rangeof interest is dispensed into a vessel, a distinct detectable lightabsorbance spectral feature exists at a wavelength and absorbance levelwithin the dynamic range of the photometric instrument. In a solutioncontaining multiple dyes, for example, the concentrations of thedifferent dyes are chosen so that a relatively large volume delivered bya liquid delivery device is calibrated using a spectral feature in thesolution with a low absorbance per unit pathlength, while a relativelysmall volume delivery is calibrated with the same sample solution butusing a different spectral feature with a high absorbance per unitpathlength.

The use of a minimal number of sample solutions suitable to calibrate ortest over an extended volume range, or over an extended dilution range,due to the multiple distinct detectable light absorbance spectralfeatures, provides a simpler user protocol with less chance for usererror and greater convenience. This resolves a problem noted in regardto at least one of the systems of the prior references, in which fourdifferent concentrations of sample solution are used to cover anextended volume or dilution range commonly delivered by various pipettesizes. This also resolves a problem noted for the MVS® system in which asubstantial number of different concentrations of sample solution mustbe used to cover an extended dilution range of 1:1 up to 1:2048.

As noted, the purpose of putting one or more dyes providing multipledistinct detectable light absorbance spectral features into a minimalnumber of sample solutions is to simplify operation of the system.Specifically, the operator does not need to choose a correspondingconcentration of dye in a solution for each delivery volume range, ordilution range, of interest, since a lesser number of solutions servesthe entire range of delivery volumes or dilution ratios. The system canuse either a vertical beam photometer or a horizontal beam photometer,and can use either a fixed or a removable measurement vessel. Thediluent can contain a dye or not. The system can be configured to testor calibrate a single delivery at a time or multiple deliveries at onceas is the case with a multi-channel delivery device.

These and other objects and advantages of the present invention will bemore readily understood in view of the following detailed description,accompanying drawings and appended claims.

BRIEF DESCRIPTION OF THE DRAWINGS

FIG. 1 is a simplified representation of an embodiment of a set ofdevices that may be used to carry out the method of the presentinvention, including a spectrophotometer and a computing system.

FIG. 2 is a simplified representation of a dispensing device to becalibrated using the sample solutions of the present invention.

FIG. 3 is a graph of the absorbance spectrum for the dye Tartrazine.

FIG. 4 is a graph of the ideal absorbance spectrum over a completeabsorbance range of an example single solution containing four dyes ofdifferent concentrations.

FIG. 5 is a graph of the actual absorbance spectrum of an example singlesolution containing two dyes over a complete absorbance range.

FIG. 6 is a graph of the actual absorbance spectrum of the examplesingle solution of FIG. 5 at four different concentrations over aspecific limited absorbance range.

DETAILED DESCRIPTION OF A PREFERRED EMBODIMENT OF THE INVENTION

An embodiment of a set of devices associated with a system suitable forconducting the steps of the methods of the present invention is shown inFIG. 1. It is to be understood that other devices performing the samefunctions may be employed without deviating from the intended functionsof the devices represented in FIG. 1, in which a volume determiningapparatus 10 includes as primary components a liquid holder 20, aspectrophotometer 30, and a computing system 40 capable of carrying outcalculations defined through computer-executable software and/orfirmware, which software or firmware may be associated with thecomputing system 40 or alternatively with a liquid dispenser such as thetype shown in FIG. 2. It is to be understood that the computing system40 and associated programming may reside in other devices of the systemincluding, for example, the spectrophotometer 30. Further, any one ormore of the example devices described herein may be integrated into asingle device without deviating from the primary aspects of theinvention.

The liquid holder 20 is a vessel that may be used to retain liquid 21 tobe analyzed. The liquid holder 20 may be placed into thespectrophotometer 30. The spectrophotometer 30 is capable of beinginstructed to initiate absorbance measurements on the liquid 21 in theliquid holder 20. These instructions may be carried out through one ormore input devices of the spectrophotometer 30 or through the computingsystem 40. The computing system 40 includes one or more input devices,such as a keyboard 41, a mouse 42, or a combination thereof, which maybe used to control the spectrophotometer 30 and/or to performcalculations of volume determination based on the absorbancemeasurements. The computing system 40, including a computer processor 43and memory storage, is configured to carry out executable-systeminstructions for volume determination. Input information and outputinformation may be viewed on a computer display 44. Optionally, a localor remote printer 45 may be employed to print out input informationand/or output information, or the information may simply be observed onthe display 44.

A liquid dispenser 100 as shown in FIG. 2 may be used for aspirating anddispensing volumes of liquid into the liquid holder 20. The liquiddispenser includes a channel member 110 and a liquid holding tip 200, orsimply, a tip 200. The liquid dispenser 100 may be any of the liquidhandling devices used by those ordinarily skilled in the art. It shouldtherefore be understood that the liquid dispenser 100 may include onechannel member 110 or may have a plurality of channel members 110, andthat regardless of the number of channel members 110 that are included,each channel member 110 may have its own tip 200. Further, the liquiddispenser 100 may be operated manually or automatically in dispensingand aspirating the liquid 21 into and out of the liquid holder 20.

While a form of photometric instrument suitable for use as part of thesystem is shown in FIG. 1 as a desktop spectrophotometer 30 device, itmay alternatively be a small, hand held device that measures absorbancethrough vessels such as liquid holder 20 containing liquid 21. Such adevice may also be a vertical beam spectrophotometer that measuresabsorbance through vessels such as the wells of microtiter plates.However, it is to be understood that the system and related method arenot limited to such a specific photometric instrument and other types ofsuch instruments may be employed including use of a flow cell with afixed pathlength, or a fiber optic probe to take an absorbancemeasurement without deviating from the basic function of the system.

A specific vessel represented as liquid holder 20 for containing asolution having a pathlength (inside diameter) of 1.8 centimeters (cm)is used for illustration purposes throughout this description. However,that is only an example and it is to be understood that the presentinvention is not limited to a specific vessel size or pathlength. Thephotometric system of the present invention includes an opticalsub-system, preferably with four filters to select four wavelengths atwhich absorbance can be measured. It is to be understood that the systemmay use more or fewer filters for measurement at different wavelengthsor may use another means of wavelength selection. The system includesfirmware embodied in the photometric instrument that is programmed tomeasure absorbance at all necessary wavelengths every time that a volumemeasurement is made. It is to be understood that the programming may bein software or embedded in hardware. It may be contained locally in thephotometric instrument, in another device, or remotely.

The system further includes a kit with one or more vessels of knownpathlength (inside diameter) containing a known amount of diluent or afill mark for the user to add diluent, one or more bottles of samplesolution that will be dispensed by a dispenser under test, and a vesselcontaining a calibration solution. The one or more vessels may or maynot be capped and/or capped and sealed.

In the example described herein in which an operator has a kit, theoperator of the system removes a vessel containing diluent from the kitof reagents, inserts it into the photometric instrument and presses the“zero” key or other corresponding initiation or activation mechanism.The instrument reads the absorbance at all four wavelengths and setsabsorbance at all four wavelengths to zero. In the simplestimplementation of this invention, the diluent contains no dye; only abuffer and preservative.

Next, the operator removes the vessel containing diluent from theinstrument, dispenses an aliquot of sample solution into the vesselusing the delivery device being tested, caps the vessel, mixes thecontents by inverting the vessel several times, and returns it into thephotometric instrument. Alternatively, the photometric instrument has abuilt-in mixing means, in which case the operator does not need toremove the vessel from the photometric instrument. In the case where themixing is accomplished by the device, the vessel may or may not includeas part of the design, a structure within the vessel to assist withmixing by generating increased turbulence when spun or otherwise movedduring the mixing step. The operator then presses the “read” key orother corresponding initiation or activation mechanism to initiate thephotometric measurement following the mixing.

In a specific example using the indicated components, the samplesolution contains four dyes, each at a different concentration. Morespecifically, each dye is selected to be appropriate for a unique rangeof dispensed volumes. The instrument reads absorbance values for thesample solution starting at the wavelength corresponding to the featurehaving the lowest absorbance per unit pathlength and if the value is outof range, the instrument would measure the absorbance at the wavelengthcorresponding to the feature with the next lowest absorbance per unitpathlength. It is to be noted that one or more of the absorbance valuesmay be out of range for the photometric instrument and so measurementsshould be taken at each of the wavelengths until a useable value isobtained. It should be noted that this example is not intended to limitthe ways the measurements are made, as they could start at anywavelength of interest and continue in any pattern until the desiredabsorbance reading is obtained.

The programming of the software or firmware of the invention isoptionally configured to automatically choose the wavelength that hasthe highest absorbance, yet which is not out of range. Using theBeer-Lambert Law, which states that the absorbance A is the product ofdye molar absorptivity ε, dye concentration C, and pathlength l:A=εCl  (0.1),

the program calculates the volumetric results based on the opticalproperties of the sample and diluent solutions at the chosen wavelength,a dimension of the vessel, the results of the absorbance measurementsand the volume of diluent in the vessel at the start, all as describedin one or more of the references incorporated herein. For ease ofdiscussion, the terms ε and C are combined to represent absorbance perunit pathlength at the wavelength of interest. It is to be understoodthat the relevant dimension of the vessel employed in the equation isdependent upon the type of spectrophotometer used. For a horizontal beammeasurement, the vessel dimension relevant to the pathlength of lightthrough the solution is the inside diameter of the vessel. For avertical beam measurement, the pathlength of light determination isdependent upon the height of the solution in the vessel, also asdescribed in one or more of the incorporated references.

The operator can repeat the dispense operation into the same vessel anumber of times. The upper limit on how many times may be set in theprogram and may depend on: 1) the maximum volume capacity of the vessel,2) the maximum absorbance limit for the instrument, 3) the minimumabsorbance change required for acceptable results, or 4) a limitingnumber that is preprogrammed.

Once the operator is finished testing a given volume, the results may besent to the printer 45, display 44 and/or a separately linked computingdevice. The mean volume, standard deviation, and coefficient ofvariation are among the types of information that may be sent to theprinter 45, display 44 and/or separately linked computing device.

The operator can test delivery devices at several different volumes ifdesired, dispensing the same sample solution into the vessel as above,subject to the limitations noted above regarding dispensing, andpreferably, as long as the smaller volumes are dispensed first and thelarger ones subsequently. The reason for this restriction is that tomeasure a small volume accurately, a spectral feature in the solutionmust have a sufficiently high absorbance per unit pathlength to get alarge enough change in absorbance to measure accurately. If, however,the operator already added so much sample solution that the absorbanceis out of range for the photometer, then the system cannot get anaccurate measure of that small volume. As stated previously, the termabsorbance per unit pathlength is the product of the molar absorptivityof the dye and the concentration of the dye. In this application, theabsorbance per unit pathlength is associated with a spectral featurewhich may or may not result from a combination of dyes.

In the Artel PCS® system, each concentration of sample solution covers aroughly four- or five-fold range of liquid delivery volumes. Therefore,a single sample solution with a single absorbance spectral feature issufficient for equipment calibration over a four- or five-fold range ofvolumes. However, if calibration over a greater volume range is desired,more than one solution is required to cover the greater range. Forexample, if a greater range of volumes were tested with a givenrelatively dilute concentration of solution suitable for relativelylarge volumes, the smaller volumes would produce too small a change ofabsorbance to be measured accurately, leading to an unacceptably largeuncertainty in the results. Or, alternatively, if the solution were mademore concentrated to boost the signal for the smaller volumes, then therelatively large volumes would produce too high an overall absorbance,leading to non-linear or non-reproducible results. The exception to thisvolume range limit is for the most dilute solutions, which are used tomeasure the largest volumes. In this case, the volume of solution beingmeasured is so large that instead of the limit being set by absorbance,it is set by the capacity of the vessel that receives the solution.

In order to address the absorbance or volume range limitation, thesimplification provided by the present system and related methodinvolves providing a dye or a plurality of dyes producing multipledistinct detectable light absorbance spectral features in a samplesolution such that the combination of detectable light absorbancespectral features in the solution allow calibration or testing over alarger volume range or dilution range of interest than would otherwisebe allowed using a single spectral feature. When a relatively largevolume is dispensed, the system uses a spectral feature with a lowabsorbance per unit pathlength as the basis for calculating the volumedispensed. When a small volume is dispensed, the system uses a spectralfeature with a high absorbance per unit pathlength as the basis forcalculating the volume dispensed. If each spectral feature can cover avolume or dilution range of about 4:1 or about 5:1, and fournon-overlapping and distinct spectral features exist within theabsorbance spectrum, then a volume range of 2 μl to 5000 μl or adilution range of 1:1 to 1:2500 can be evaluated for a delivery deviceusing only one sample solution containing all four such spectralfeatures. By incorporating multiple spectral features into one samplesolution, the testable volume range is significantly expanded ascompared to the sample solutions used by either of the PCS® or the MVS®systems.

For the purpose of making an absorbance measurement, it is alwaysdesirable to measure at a wavelength where the spectrum has zero slope,so that a slight error in wavelength will result in little or nocorresponding error in absorbance value. Zero slope occurs either at aminimum or a maximum or a plateau in the absorbance spectrum. A singlesample solution created through the present system with a dye or aplurality of dyes should provide a complete absorbance spectrum with atleast four distinct detectable light absorbance spectral features (i.e.,any combination of peaks and/or valleys and/or plateaus) where the slopeat each spectral feature is zero. The absorbance values for the peaks orvalleys or plateaus must fall within a defined absorbance range which issuitable for measuring a designated range of volumes. If a combinationof four different dyes is chosen, then there is complete control overthe magnitude of absorbance at all four peaks and/or valleys and/orplateaus. On the other hand, it may be possible to use a single dyehaving two or more distinct detectable light absorbance spectralfeatures that happen to have suitable magnitudes, but the relationshipbetween the magnitudes of each feature is beyond the control of theuser.

By way of example and not intending to be limiting, Table 1 summarizesdesign parameters based on a system using four absorbance peaks, a pathlength of 1.8 cm; a maximum absorbance of 1.5 Optical Density (OD); anda diluent volume of 5000 μl. One skilled in the art would recognize thatthe term Optical Density (OD) could also be referred to as AbsorbanceUnits (AU) or Extinction (E).

TABLE 1 Volume range of Absorbance of sample Measured Absorbance for theliquid dispenser solution per cm at the smallest volume in the rangebeing tested wavelength of interest (must exceed 0.05 OD) 2-10 μl 84.2at 520 nm 0.061 10-50 μl 17.5 at 430 nm 0.063 50-200 μl 5.00 at 730 nm0.086 200-5000 μl 1.67 at 630 nm 0.101

Most simple and reasonably priced photometric instruments are able tomeasure in the visible and near infrared region of the spectrum. Glassabsorbs light at ultraviolet wavelengths and silicon photodiodes are notas sensitive at that part of the spectrum. A special source is requiredfor UV wavelengths, typically a deuterium lamp, which would add to thecost of the system. The most basic system will stay within thewavelength range of 340 to 800 nanometers (nm). The dyes chosen for theexamples given in this disclosure have principal peaks within thisrange; however there is no reason that dyes with peaks or valleys orplateaus outside of this range could not be used, provided they wereused in conjunction with an instrument that could measure in theexpanded range.

Many organic dyes have an absorbance spectrum with a principal peak atone wavelength, and lesser peaks and valleys at shorter wavelengthswhich need to be considered when combining dyes. Often, the absorbancedecreases sharply to zero at wavelengths longer than the principal peak.An example of such a spectrum is that for Tartrazine, represented by theabsorbance curve shown in FIG. 3, in which the principal peak is atabout 425 nm. This property is useful when combining multiple dyes inone sample solution since, when the most concentrated dye is chosen tobe the one at the short end of the wavelength range, it does notinterfere with the spectra of the dyes that are added with principalabsorbance peaks at longer wavelengths. In this way, multiple dyes canbe combined in a way that their spectra have relatively littleinterference with one another.

Two examples of sample solutions with multiple distinct detectable lightabsorbance spectral features are described herein; one uses four dyesand the other uses two. These are only examples and are not intended torepresent all options for using one or more dyes in a single samplesolution to establish multiple distinct detectable light absorbancespectral features.

The four dyes of the first example are chosen based on the followingcriteria:

Peaks are approximately equally spaced and are within the visible rangewhen the dyes are combined;

Peaks are broad enough so that they are easily measured with aninstrument of modest wavelength accuracy (e.g. ±5 nm);

They are all adequately soluble in aqueous solution;

Their physical properties in aqueous solution do not adversely affectthe ability of a liquid delivery device to accurately dispense theresulting solution (e.g. if surface tension of the solution is reduced,there will be a tendency for small droplets to remain behind in the tipof the delivery device);

They are not unstable in solution (e.g. due to light exposure) or pHdependent (e.g. indicators); and

The tail on the long wavelength side of the principal peak of one dyedoes not overlap with the peak of the next dye. This helps to assurethat the next peak really is a peak, and not just a bump on the tail ofthe peak below it.

In the conceptually simplest example of a single solution containingfour dyes, there are four peaks and each peak does not interfere withits neighboring peaks. The absorbance spectral features for thisfour-dye example are represented in FIG. 4. In that figure, Feature 1,which is the peak for Cu(EDTA)²⁻ and has the lowest absorbance per unitpathlength of the four dyes, could be used for the largest volumes(200-5000 μl) to be tested. Feature 2, which is the peak for MethylGreen, could be used for the next volume range down (50-200 μl). Feature3, which is the peak for Ponceau S, could be used for the next volumerange down (10-50 μl). Finally, Feature 4, which is the peak forTartrazine and has the highest absorbance per unit pathlength of thefour dyes, could be used for the smallest volumes (2-10 μl) to betested.

The four dyes used in this example and meeting the criteria identifiedabove are given in Table 2:

TABLE 2 Wavelength at Peak Desired absorbance Dye Absorbance per cmCu(EDTA)²⁻ 730 nm 1.67 Methyl Green 629 nm 5.00 Ponceau S 520 nm 17.5Tartrazine 425 nm 84.2Dilution ratios for the concentrations of this sample solution whichtarget each dye are 0.5 for the Cu(EDTA)²⁻, 0.17 for the Methyl Green,0.05 for the Ponceau S, and 0.01 for the Tartrazine. It is to beunderstood that other dyes may be used, other or the same dyes may beused in different concentrations, to achieve the intended outcome of thepresent invention and that the example represented in the table is in noway intended to be limiting.

In the event the four-dye relationship shown in FIG. 4 is difficult toachieve, such as due to limitations of the spectrophotometer or the dyesavailable, a smaller number of dyes may be used, provided theircharacteristics provide the desired number of distinct detectable lightabsorbance spectral features to cover the volume ranges of interest. Anexample alternative for that purpose is the two-dye combinationrepresented in FIGS. 5 and 6. FIG. 5 represents the absorbance curve forthe two-dye sample solution for a complete absorbance range using alogarithmic scale and FIG. 6 represents four different dilutions of thetwo-dye sample solution, each dilution being chosen to bring one of thespectral features within the absorbance range typically available withcommercial photometric instruments. In this alternative example, the twodyes produce two peaks and two valleys to give distinct spectralfeatures from which to calculate the volume dispensed. Feature 1, avalley between the peak of the Cu(EDTA)²⁻ and the principal Ponceau Speak, could be used for the largest volumes (200-5000 μl). Feature 2,the Cu(EDTA)²⁻ peak, could be used for the next volume range down(50-200 μl). Feature 3, a valley from the Ponceau S minimum between theprincipal and secondary peaks, could be used for the next range (10-50μl). Finally, Feature 4, the principal Ponceau S peak could be used forthe smallest volumes (2-10 μl).

The two dyes used for this example have the characteristics given Table3:

TABLE 3 Desired Wavelength of absorbance Dye/Spectral Feature Featureper cm Cu(EDTA)²⁻ 730 nm 5.00 Valley between Cu(EDTA)²⁻ 629 nm 2.68 andPonceau S Ponceau S 520 nm 84.2 Ponceau S Valley 425 nm 18.2In this example, the desired absorbance per cm for the valley betweenthe Cu(EDTA)²⁻ and Ponceau S is fixed based on the ratio of the two dyesin the solution. Also, the absorbance per cm for the Ponceau S valley isrelated to the absorbance per cm of the peak as it is a property of thatdye.

The results of a volume measurement using a multi-dye solution of thepresent invention are calculated using the Beer Lambert Law identifiedin equation (0.1) herein. Specifically, for the first delivery of samplesolution with volume V₁ the expected absorbance at wavelength i is

$\begin{matrix}{A_{1}^{i} = {ɛ_{i}C_{i}{l\left( \frac{V_{1}}{V_{1} + V_{D}} \right)}}} & (0.2)\end{matrix}$

Where A₁ ^(i) is the absorbance after the first delivery measured atwavelength i, ε_(i)C_(i) is the absorbance per unit pathlength of thesample solution at wavelength i; and V_(D) is the volume of diluentoriginally in the vessel.

This can be solved for the delivery volume V₁:

$\begin{matrix}{V_{1} = {V_{D}\left( \frac{A_{1}^{i}}{{ɛ_{i}C_{i}l} - A_{1}^{i}} \right)}} & (0.3)\end{matrix}$

This equation holds for all of the absorbance measurements at allwavelengths. However, some of the absorbance measurements are unsuitablefor use; either they are so small that there is too much uncertaintyassociated with them, or they are too large for the instrument tomeasure accurately. If the concentrations of the different dyes havebeen chosen correctly, then at least one of the absorbance measurementsis in a measurable absorbance range and can be used to calculate anaccurate value of volume.

After the n^(th) delivery of sample solution, the total volume of samplesolution delivered up to and including the n^(th) can be calculated inthe same way:

$\begin{matrix}{{{V_{T}(n)} \equiv {\sum\limits_{j = 1}^{n}V_{j}}} = {V_{D}\left( \frac{A_{n}^{i}}{{ɛ_{i}C_{i}l} - A_{n}^{i}} \right)}} & (0.4)\end{matrix}$The system of the present invention includes the option, manually orautomatically through programming, such as associated with the firmware,for example, but not limited thereto, to keep a running tally of howmuch sample has been added through the n−1^(th) delivery, so it cansimply be subtracted to find the value added at the n^(th) delivery:

$\begin{matrix}{{V_{n} \equiv {{V_{T}(n)} - {V_{T}\left( {n - 1} \right)}}} = {V_{D}\left( {\frac{A_{n}^{i}}{{ɛ_{i}C_{i}l} - A_{n}^{i}} - \frac{A_{n - 1}^{j}}{{ɛ_{j}C_{j}l} - A_{n - 1}^{j}}} \right)}} & (0.5)\end{matrix}$Note that the value of V_(n) is only dependent on the n^(th) andn−1^(th) absorbance measurements, and that these two sequentialmeasurements need not have been made at the same wavelength. In equation(0.5) the n^(th) measurement was made at wavelength i, and the n−1^(th)was made at wavelength j.

An example of how volumetric results could be calculated for the examplecase of four dyes noted above follows. In this example, the userdispenses one aliquot of 5 μl, one of 20 μl, one of 100 μl and one of1000 μl. The initial volume of diluent is 5000 μl. The vessel pathlengthis 1.8 cm. The expected absorbance values at the four wavelengths andthe calculated volumes are provided in Table 4:

TABLE 4 Volume of Diluent 5000 ul Pathlength 1.8 cm Max absorbance 1.5Total Total Volume Abs per cm Calculated Calculated Volume Added SampleVolume in Vial Wavelength of Sample Sol'n Absorbance Total Sample SampleAdded  5 5 5005 730 1.67 0.003003 5 5005 629 5 0.008991 5 5005 520 17.50.031469 5 5005 425 84.2 0.151409 5 5 20 25 5025 730 1.67 0.014955 255025 629 5 0.044776 25 5025 520 17.5 0.156716 25 5025 425 84.2 0.7540325 20 100  125 5125 730 1.67 0.073317 125 5125 629 5 0.219512 125 5125520 17.5 0.768293 125 100 125 5125 425 84.2 3.696585 1000  1125 6125 7301.67 0.552122 1125 1000 1125 6125 629 5 1.653061 1125 6125 520 17.55.785714 1125 6125 425 84.2 27.83755

Table 4 gives the absorbance values at each of the four wavelengthsafter each delivery. For each volume determination, the absorbanceselected for use in the calculation is the one that is as large aspossible yet also within the measurable absorbance range (less than 1.5in this example). Those values are shown in the table. In making thecalculation, the absorbance per cm for the spectral feature at themeasured wavelength is used in the equations above.

The scenarios presented above have described using multiple lightabsorbance spectral features present in the sample solution to determinethe accuracy of volume delivery from a test device. The examplespresented demonstrate that by using multiple light absorbance spectralfeatures in the sample solution, a significantly enlarged testablevolume range can be achieved, as compared to individual solutions withonly one light absorbance spectral feature. Yet another way to furtherexpand the testable volume range would be to include one or a pluralityof dyes in the diluent solution, which present one or a plurality ofdistinct light absorbance spectral features, these features being uniqueto the diluent solution. Because these light absorbance spectralfeatures are unique to the diluent solution, they are not in commonwith, nor overlap significantly with any light absorbance spectralfeature or features in the sample solution. The light absorbancespectral features in the diluent can also be used to quantify volumeadditions.

As an example of this alternative approach, the absorbance values of thelight absorbance spectral features in the diluent are measured prior toany sample volume addition. As in the examples above, some of thesefeatures will be too highly absorbing, but others will be within range.The desired test volume of sample solution is then added to the diluentand mixed, and the absorbance values of the light absorbance spectralfeatures in the mixture of sample and diluent are measured. The additionof sample solution dilutes the concentration of dyes in the diluent,reducing the absorbance values for the light absorbance spectralfeatures of the diluent dyes. The decrease in absorbance for the diluentspectral features in the mixture is directly related to the volume ofsample solution that was added. Thus, by applying the same concepts asexplained for the sample solution above, multiple light absorbancespectral features in the diluent can be used to measure sample volume.

A clear extension of the above example would be to use a sample solutionwith multiple light absorbance spectral features as well as a diluentwith multiple light absorbance spectral features that are unique to thediluent and different from the sample. By monitoring the absorbance ofthe multiple light absorbance spectral features in the sample and in thediluent, an even further extension of testable volume range can beachieved. Because the light absorbance spectral features in the diluentare measured by their dilution, measurable changes to these featuresoccur typically due to larger sample volume additions. Thus, thefeatures in the diluent should be most applicable to large sample volumeadditions, whereas the small sample volume additions will be moreappropriately measured by the light absorbance spectral features in thesample solution.

It can be seen from this alternative example that the present inventionmay be used to calculate the volume of a sample solution added to avessel wherein the sample solution may include one or a plurality ofdyes presenting one or a plurality of distinct light absorbance spectralfeatures, the diluent may also include one or more dyes presenting oneor a plurality of distinct light absorbance spectral features, furtherdistinct from the features of the sample solution, all in anycombination to cover a wider range of volumes than has heretofore beenavailable.

It is desirable that means be provided to allow the user to periodicallytest the instrument for correct and accurate functionality. One methodof doing that is to provide a vessel containing calibration solution inthe reagent kit. This calibration solution preferably contains all ofthe same dyes present in the sample solution(s); however, theconcentrations will be such that the absorbance values are within ameasurable range at all of the wavelengths without dilution, at leastwith respect to the four-dye example. The user inserts the vessel intothe instrument, and instructs it to check the calibration. Readings aremade at all of the wavelengths and compared to the values measured inthe kit manufacturer's laboratory using an instrument whose results aretraceable to international standards. Pass/Fail criteria are provided bythe manufacturer of the system. The calibration vessel will not beconsumed or altered in this process, so the calibration can be carriedout as often as desired. For the situation in which fewer than four dyesare used, more than one calibration standard might be required in orderto provide a calibration point within the measurable absorbance rangefor each utilized wavelength.

As previously indicated, the concept of using one or more samplesolutions, with each sample solution including multiple light absorbancespectral features, may also be applied to evaluations of dilutionprotocols. U.S. patent application Ser. No. 11/854,594 incorporatedherein provides details of three dilution-related methods involving theuse of different calculation mechanisms for determining either volume ordilution ratios based on dilution protocols performed. The referencedescribes dilution evaluations based on the use of a single lightabsorbance spectral feature in solutions used to carry out thedeterminations. The present invention includes methods in whichsolutions having multiple light absorbance spectral features are used inthe dilution evaluations in which a sample solution is combined with adiluent one or more times.

A first dilution-related method provides the capability to measure thevolume of a sample solution in a vessel over a volume range that iswider than can be measured when a single light absorbance spectralfeature component is employed while also eliminating uncertainty due tovessel dimension variability. Specifically, the first dilution-relatedmethod for use with a vessel having a bottom and known dimensions,includes the steps of: a) adding to the vessel a diluent including aknown concentration of a diluent dye, resulting in a diluent with alight absorbance spectral feature at a wavelength unique to the diluentand having no measurable absorbance at the wavelengths of interest forthe sample solution; b) measuring the absorbance at the wavelengthunique to the diluent; c) adding a volume of the sample solution to thevessel, wherein the sample solution has no measurable absorbance at thewavelength unique to the diluent, and includes one or more dyes, atknown concentration(s), to establish multiple light absorbance spectralfeatures at a corresponding plurality of wavelengths; d) mixing thediluent and the sample solution in the vessel to produce a mixture ofthe sample solution and the diluent; e) measuring the absorbance of themixture of the sample solution and the diluent at all wavelengths; andf) calculating the volume of the sample solution added to the vesselbased on the measured absorbance values.

Calculating the volume in the first dilution-related method requiresthat the volume of diluent added to the vessel be known. If it is notknown, it is calculated from the absorbance per unit pathlength of thediluent at the wavelength unique to the diluent, the pathlength of lightthrough the diluent as determined using the measured absorbance of thediluent dye at the wavelength, prior to adding the sample solution tothe vessel, and the dimensions of the vessel. The first dilution-relatedmethod includes using the following equation to calculate the volume:

$\begin{matrix}{V_{s} = {V_{d} \cdot \frac{a_{d}}{a_{s}} \cdot \frac{A_{\lambda\; 1}}{A_{\lambda\; 2}}}} & (0.6)\end{matrix}$where (V_(s)) is the volume of the sample solution added to the vessel,(V_(d)) is the volume of the diluent added to the vessel, (a_(d)) is theabsorbance per unit pathlength of the spectral feature in the diluent,(a_(s)) is the absorbance per unit pathlength of a spectral feature ofthe sample solution having a measurable absorbance for a volume range,(A_(λ1)) is the absorbance of the spectral feature of the samplesolution at a wavelength that is measurable, and (A_(λ2)) is theabsorbance of the spectral feature in the diluent at the wavelengthdistinct from the measurable wavelength of the spectral feature of thesample solution. That is, the single sample solution may be used over abroad volume range by providing at least one distinct light absorbancespectral feature per volume range subset without requiring replacementof a first sample solution with one known dye concentration with asecond sample solution with a second known concentration of the samedye, which second concentration is greater or less than the knownconcentration of the first sample solution. In the example previouslydescribed regarding a sample solution with four dyes, the samplesolution may be employed in the first dilution-related method for volumemeasurements over a volume range that would previously have only beenachievable with four separate sample solutions, each having a singledistinct light absorbance spectral feature. Similarly, the two-dyesample solution from above could cover the same volume range becauseeach dye results in two distinct detectable light absorbance features,for a total of four distinct spectral features in the solution, witheach distinct feature covering a different volume range.

An additional approach that can be added to this first dilution-relatedmethod is to incorporate multiple dyes into the diluent which impartmultiple light absorbance spectral features to the diluent which areunique to the diluent and different from the light absorbance spectralfeatures present in the sample solution. The added light absorbancespectral features of the diluent provide the capability to measure thevolume of a sample solution in a vessel over a volume range that iswider than can be measured when only light absorbance spectral featuresin the sample are used. This approach involves the steps of: a) addingto the vessel a diluent including a known concentration orconcentrations of one or a plurality of diluent dyes, resulting in adiluent with a plurality of light absorbance spectral features atwavelengths unique to the diluent and having no measurable absorbance atthe wavelengths of interest for the sample solution; b) measuring theabsorbance at the wavelengths unique to the diluent; c) adding a volumeof the sample solution to the vessel, wherein the sample solution has nomeasurable absorbance at the wavelengths unique to the diluent, andincludes one or more dyes, at known concentration(s), to establishmultiple light absorbance spectral features at a corresponding pluralityof wavelengths; d) mixing the diluent and the sample solution in thevessel to produce a mixture of the sample solution and the diluent; e)measuring the absorbance of the mixture of the sample solution and thediluent at all wavelengths; and f) calculating the volume of the samplesolution added to the vessel based on the measured absorbance values.

A second dilution-related method of the present invention provides thecapability to determine the dilution of a sample solution over a volumerange or a dilution range that is wider than is available in a similarvolume or dilution determination when only a single light absorbancespectral feature can be measured. The sample solution includes aplurality of dyes and the diluent includes a dye that is the same as oneof the plurality of dyes of the sample solution and is included insubstantially the same concentration as in the sample solution for thatcommon dye. Specifically, the second dilution-related method includesthe steps of: a) measuring in the sample solution the absorbance valuesof each of the plurality of spectral features at respective independentwavelengths for which measurable absorbance values may be obtained,wherein the sample solution is contained in a first vessel of aplurality of vessels; b) transferring a target volume of the samplesolution from the first vessel to a second vessel of the plurality ofvessels; c) mixing into the sample solution in the second vessel atarget volume of the diluent; d) measuring the absorbance values of thespectral features in the second vessel for which measurable absorbancevalues may be obtained, but for which a measurable absorbance must beobtained for the common dye; and e) calculating a dilution ratio for thesample solution contained in the second vessel, wherein the dilutionratio represents the extent to which the sample solution has beendiluted by the diluent mixed into the second vessel.

The calculation of the dilution ratio associated with the transfer ofthe sample solution from the first vessel into the second vessel, andthen diluting that mixture involves using the equation

$\begin{matrix}{R_{12} = {\frac{A_{1,{\lambda\; 1}}}{A_{2,{\lambda\; 1}}} \cdot \frac{A_{2,{\lambda\; 2}}}{A_{1,{\lambda\; 2}}}}} & (0.7)\end{matrix}$where (A_(1,λ1)) is the absorbance of any of the plurality of spectralfeatures, only of the sample solution, that provide an absorbance withina defined measurable absorbance range and that are measured in the firstvessel, (A_(2,λ1)) is the absorbance of any of the plurality of spectralfeatures, only of the sample solution, that provide an absorbance withina defined measurable absorbance range and that are measured in thesecond vessel, (A_(1,λ2)) is the absorbance of the spectral feature thatis common to both the sample solution and the diluent measured in thefirst vessel containing only the sample solution, (A_(2,λ2)) is theabsorbance of the spectral feature that is common to both the samplesolution and the diluent measured in the second vessel, and (R₁₂) is thedilution ratio.

The second dilution-related method may be extended across furtherdilution steps beyond a transfer from the first vessel to the secondvessel by: a) repeating X more times the steps of i) transferring atarget volume of the mixture of the sample solution and the diluent intoa subsequent vessel, ii) mixing in a target volume of the diluent intothe subsequent vessel, and iii) measuring the absorbance values for allspectral features for which measurable absorbance values may beobtained, wherein X is ≧1, such that the last vessel of the plurality ofvessels with the mixture of the sample solution and the diluent and theadded diluent is vessel n and a preceding vessel is vessel m; and b)calculating a dilution ratio for the mixture of the sample solution andthe diluent contained in vessel n, wherein the dilution ratio representsthe extent to which the mixture of the sample solution and the diluenthas been diluted by the diluent mixed into vessel n. A running tally maybe kept of how much diluted sample has been added from a precedingvessel into a specific vessel through the n^(th) delivery based on thedilution ratio. The dilution ratio may be calculated for any number ofdilution steps of a dilution protocol across a relatively larger volumerange with the second dilution-related method of the present inventionusing the equation

$\begin{matrix}{R_{mn} = {\frac{A_{m,{\lambda\; 1}}}{A_{n,{\lambda\; 1}}} \cdot \frac{A_{n,{\lambda\; 2}}}{A_{m,{\lambda\; 2}}}}} & (0.8)\end{matrix}$where (R_(mn)) is the dilution ratio for the mixture of the samplesolution and the diluent in vessel m after mixing with the diluent invessel n, (A_(m,λ1)) is the measurable absorbance of any of theplurality of spectral features only of the sample solution measured invessel m, (A_(n,λ1)) is the measurable absorbance of any of theplurality of spectral features only of the sample solution measured invessel n, (A_(m,λ2)) is the absorbance of the spectral feature that iscommon to both the sample solution and the diluent measured in vessel m,and (A_(n,λ2)) is the absorbance of the spectral feature that is commonto both the sample solution and the diluent measured in vessel n.

It can be seen that a single sample solution may be diluted over a broadvolume range by providing at least one distinct light absorbancespectral feature per volume range subset without requiring replacementof a first sample solution with one known dye concentration with asecond sample solution with a second known concentration of the samedye, which second concentration is greater or less than the knownconcentration of the first sample solution. In the example previouslydescribed regarding a sample solution with four dyes, the samplesolution may be employed in the second dilution-related method, providedit also included a fifth dye with a distinct measurable light absorbancespectral feature in common with the dye of the diluent, to assessdilution over a volume range that would previously have only beenachievable with four separate sample solutions, each having a singledistinct light absorbance spectral feature (again, each being distinctfrom the light absorbance spectral feature of the dye in common with thedye of the diluent). Similarly, the two-dye sample solution example fromabove could cover the same volume range if a third dye were added, whichthird dye would be present in both the sample solution and the diluentin substantially equal concentrations. In using either a four-dye or atwo-dye version of the invention, this second dilution-related methodmay be used to reduce uncertainty due to variable dilution volume, orvariable vessel pathlength, for example, when used for testing inmicrotiter plates measured using vertical beam spectrophotometers.

In an example of the second dilution-related method, a single samplesolution and a single diluent could be mixed together and used tocalculate the dilution of the sample solution by the diluent over acomplete volume range.

A third dilution-related method of the present invention provides acapability similar to that of the second dilution-related method inorder to determine the dilution of a sample solution over a volume rangeand a dilution range that is wider than is available in a similarcorresponding dilution determination when only a single light absorbancespectral feature can be measured. The sample solution includes aplurality of dyes and the diluent includes a dye that is the same as oneof the plurality of dyes of the sample solution and is included insubstantially the same concentration as in the sample solution for thatcommon dye. Specifically, the third dilution-related method includes thesteps of: a) transferring a target volume of the sample solution from asource into a vessel; b) mixing into the sample solution in the vessel atarget volume of the diluent; c) measuring the absorbance values of thespectral features of the solution in the vessel; and d) calculating adilution ratio of the sample solution from the source, wherein thedilution ratio represents the extent to which the sample solution of thesource has been diluted by the diluent mixed into the vessel.

The third dilution-related method may be extended across furtherdilution steps beyond a transfer from the source to a single vessel by:a) repeating X more times the steps of i) transferring a target volumeof the mixture of the sample solution and the diluent to a subsequentvessel, ii) adding a target volume of the diluent with the knownconcentration of the common dye to the mixture of the sample solutionand the diluent in the subsequent vessel and iii) measuring theabsorbance values, wherein X is ≧1, such that any vessel but the sourceis vessel m and the source is represented as vessel 0; and b)calculating a dilution ratio for the sample solution from the source,wherein the dilution ratio represents the extent to which the samplesolution of the source has been diluted by the diluent through allmixing steps. The dilution ratio may be calculated for any number ofdilution steps of a dilution protocol across a relatively larger volumerange with the third dilution-related method of the present inventionusing the equation

$\begin{matrix}{R_{0m} = {\frac{a_{s}}{a_{d}} \cdot \frac{A_{m,{\lambda\; 2}}}{A_{m,{\lambda\; 1}}}}} & (0.9)\end{matrix}$where (R_(0m)) is the dilution ratio for the sample solution of vessel 0after all diluent additions, (a_(d)) is the absorbance per unitpathlength of the common spectral feature, (a_(s)) is the absorbance perunit pathlength of a spectral feature unique to the sample solution,(A_(m,λ1)) is the measurable absorbance of the spectral feature uniqueto the sample solution measured in vessel m, and (A_(m,λ2)) is themeasurable absorbance of the common spectral feature measured in vesselm.

It can be seen that a single sample solution may be diluted over a broadvolume range by providing at least one distinct light absorbancespectral feature per volume range subset without requiring replacementof a first sample solution with one known dye concentration with asecond sample solution with a second known concentration of the samedye, which second concentration is greater or less than the knownconcentration of the first sample solution. In the example previouslydescribed regarding a sample solution with four dyes, the samplesolution may be employed in the third dilution-related method, providedit also includes a fifth dye with a distinct measurable light absorbancefeature in common with the spectral feature of the diluent, to assessdilution over a volume range that would previously have only beenachievable with four separate sample solutions, each having a singledistinct light absorbance spectral feature (again, each being distinctfrom the light absorbance spectral feature of the dye in common with thedye of the diluent).

In an example of the third dilution-related method, a single samplesolution and a single diluent could be mixed together and used tocalculate the dilution of the sample solution by the diluent over acomplete volume range.

A fourth dilution-related method of the present invention provides acapability similar to that of the second and third dilution-relatedmethods in order to determine the dilution of a sample solution over avolume range and a dilution range that is wider than is available in asimilar corresponding dilution determination when only a single lightabsorbance spectral feature can be measured. This fourth dilutionrelated method is similar to the second dilution related method in thatit can be used to determine the dilution ratio between any two steps ina multiple dilution step protocol. However, this fourth approach isneeded because the dilution steps are too large to allow for an accuratedetermination of the dilution ratio using equation (0.8). In this fourthdilution-related method, a multi-step dilution protocol is conducted.The sample solution includes a plurality of dyes and the diluentincludes a dye that is the same as one of the plurality of dyes of thesample solution and is included in substantially the same concentrationas in the sample solution. Specifically, the fourth dilution-relatedmethod includes the steps of: a) transferring a target volume of thesample solution from a source into a first vessel; b) mixing into thesample solution in the first vessel a target volume of the diluent; c)transferring a target volume of the mixed sample and diluent from thefirst vessel into a second vessel, d) mixing into the solution in thesecond vessel a target volume of the diluent, e) measuring theabsorbance values of the spectral features of the solution in the firstand second vessels; and f) calculating a dilution ratio for the samplesolution contained in the second vessel, wherein the dilution ratiorepresents the extent to which the mixed sample and diluent from thefirst vessel has been diluted by the diluent mixed into the secondvessel.

This fourth dilution-related method requires a different calculationbecause neither equation (0.8) nor equation (0.9) is capable ofdetermining the described dilution protocol under all conditions. Forexample, assume that the delivery of solution from the first vessel tothe second vessel involves a dilution step that is larger than can bemeasured by any one absorbance spectral feature. When usingabsorbance-based dyes, a measurable linear absorbance can typically onlybe achieved over a concentration change of 2-3 orders of magnitude.Thus, assume a scenario where the delivery from the source to the firstvessel is large. In this case, one light absorbance spectral feature,which will be called s is selected for the analysis. The absorbance perunit pathlength of s is known for the undiluted solution in the sourcevessel and is given by a_(s). Since the dilution of the sample solutionfrom the source vessel to the first vessel is sufficiently large,equation (0.8) cannot be used to determine the dilution that has beenperformed because the absorbance associated with s will be too high todirectly measure for the sample solution in the source vessel. However,assuming the dilution step results in a measurable absorbance associatedwith s in the first vessel, equation (0.9) can be used to determine thedilution that has occurred. Now, assume that the dilution protocol iscarried out from the first vessel into the second vessel, and that thisdilution step is also large. In this scenario, the absorbance associatedwith s is measurable in the first vessel, but the dilution protocol mayhave caused the absorbance associated with s to be too small to beaccurately measured in the second vessel.

Because the absorbance associated with s cannot be accurately measuredin the second vessel, the dilution cannot be determined using any of theequations presented so far. A new equation needs to be considered forsuch a scenario, which involves using a second absorbance spectralfeature, which will be called s′. The absorbance per unit pathlength ofs and s′ are known for the sample solution in the source vessel, but aresufficiently large such that the absorbance values of s and s′ cannot bedirectly measured solely for the undiluted sample solution. Asdescribed, the dilution that occurs in transferring the sample solutionfrom the source vessel into the first vessel results in a measurableabsorbance associated with s. However, in this case, the absorbanceassociated with s′ is still too large to be measurable. Continuing theprotocol between the first vessel and the second vessel results in anabsorbance associated with s that is too small to be accuratelymeasured, but results in a measurable absorbance associated with s′. Forthis scenario, the dilution of the sample solution that occurs betweenthe first vessel and the second vessel can be determined by dividing theoverall dilution between the source vessel and the second vessel by theoverall dilution between the source vessel and the first vessel, asexpressed by:

$\begin{matrix}{R_{12}^{\prime} = \frac{R_{02}}{R_{01}}} & (1.0)\end{matrix}$where (R₀₁) is calculated using equation (0.9) with the first vessel asvessel m, the wavelength associated with the common spectral feature inthe diluent is λ₂ and the wavelength associated with the spectralfeature s that is unique to the sample solution is λ₁. Similarly, (R₀₂)is calculated using equation (0.9) with the second vessel as vessel mand the wavelength associated with the common spectral feature in thediluent is λ₂ and the wavelength associated with the spectral feature s′that is unique to the sample solution is λ₁.

The fourth dilution-related method may be extended across furtherdilution steps beyond a transfer from the first vessel to the secondvessel by: a) repeating X more times the steps of i) transferring atarget volume of the mixture of the sample solution and the diluent intoa subsequent vessel, ii) mixing in a target volume of the diluent intothe subsequent vessel, and iii) measuring the absorbance values for allspectral features for which measurable absorbance values may beobtained, wherein X is ≧1, such that the last vessel of the plurality ofvessels with the mixture of the sample solution and the diluent and theadded diluent is vessel n and a preceding vessel is vessel m; and b)calculating a dilution ratio for the mixture of the sample solution andthe diluent contained in vessel n, wherein the dilution ratio representsthe extent to which the mixture of the sample solution and the diluenthas been diluted by the diluent mixed into vessel n. The dilution ratiomay be calculated for any number of dilution steps of a dilutionprotocol across a volume range with the fourth dilution-related methodof the present invention using the equation

$\begin{matrix}{R_{mn}^{\prime} = \frac{R_{0n}}{R_{0m}}} & (1.1)\end{matrix}$where (R′_(mn)) is the dilution ratio that has occurred as the mixtureof sample solution and diluent is transferred from vessel m and mixedinto the diluent in vessel n. This equation is a quotient of equation(0.9) expressed for the overall dilution from the source vessel, denotedby the subscript 0, to vessel n, and also equation (0.9) expressed forthe overall dilution from the source vessel to vessel m, which directlyprecedes vessel n in the dilution protocol. A more useful form ofequation (1.1) can be derived by substitution of the terms in equation(0.9) and algebraically simplifying to give:

$\begin{matrix}{R_{mn}^{\prime} = {\frac{a_{s^{\prime}}}{a_{s}} \cdot \frac{A_{m,\lambda_{s}}}{A_{m,\lambda_{d}}} \cdot \frac{A_{n.\lambda_{d}}}{A_{n,\lambda_{s^{\prime}}}}}} & (1.2)\end{matrix}$where (a_(s)) is the absorbance per unit pathlength of the spectralfeature s, unique to the sample solution, which results in a measurableabsorbance in vessel m, (a_(s′)) is the absorbance per unit pathlengthof the spectral feature s′, also unique to the sample solution butdifferent than spectral feature s, which results in a measurableabsorbance in vessel n, (A_(m,λs)) is the measured absorbance in vesselm at the wavelength λ_(s) which corresponds to the spectral feature s ofthe sample solution, (A_(m,λd)) is the measured absorbance in vessel mat the wavelength λ_(d) which corresponds to the spectral feature thatis common between the sample and diluent solutions, (A_(n,λd)) is themeasured absorbance in vessel n at the wavelength λ_(d) whichcorresponds to the spectral feature that is common between the sampleand diluent solutions, (A_(n,λs′)) is the measured absorbance in vesseln at the wavelength λ_(s′) which corresponds to the spectral feature s′of the sample solution.

By using a solution containing multiple dyes and multiple lightabsorbance spectral features, dilution ratios for all steps of adilution scheme can be measured using equations (0.8), (0.9) and (1.2).Not all spectral features will be within the measurable absorbance rangeof the spectrophotometer. However, while one spectral feature may resultin measurable absorbance values within the first few dilution steps,another spectral feature would provide measurable absorbance values onlyafter multiple steps in the dilution scheme have already been made.Thus, if the dilution method is followed and different spectral featuresare used, the accuracy of each step can be determined.

The present invention may further be used to determine volume throughfeatures associated with a diluent as follows. A method of the inventionfor determining a liquid volume of a sample solution in a vessel,wherein the vessel includes a bottom and known dimensions, involves thesteps of: a) adding to the vessel a diluent including a knownconcentration or concentrations of one or more diluent dyes, resultingin a diluent with multiple light absorbance spectral features at acorresponding number of distinct wavelengths; b) measuring absorbance atone or more of the distinct wavelengths; c) adding a volume of thesample solution to the vessel, wherein the sample solution has nomeasurable absorbance at the distinct wavelengths of the multiple lightabsorbance spectral features of the diluent; d) mixing the diluent andthe sample solution in the vessel to produce a mixture of the samplesolution and the diluent; e) measuring measurable absorbances of themixture of the sample solution and the diluent; and f) calculating thevolume of the sample solution added to the vessel based on the measuredabsorbances. In this method, the sample solution may contain no dye orone dye having one light absorbance spectral feature at a correspondingwavelength distinct from any wavelength of the distinct wavelengths ofthe multiple spectral features of the diluent. Alternatively, the samplesolution may contain one or more dyes producing a plurality of lightabsorbance spectral features at corresponding distinct wavelengths. Thedistinct wavelengths of the light absorbance spectral features of theone or more dyes of the sample solution may all be different from thedistinct wavelengths of the multiple spectral features of the diluent,or one of the distinct wavelengths of the light absorbance spectralfeatures of the one or more dyes of the sample solution may be the sameas one of the distinct wavelengths of the multiple spectral features ofthe diluent.

It is further to be noted that the present invention includes a systemfor testing or calibrating a liquid delivery volume comprising at leasta portion of the following:

a photometric measurement means that measures optical absorbance at morethan one wavelength and which is capable of communicating results to anexternal printer or computer,

one or more sample solutions that are delivered by the device beingtested, each sample solution containing one or more dyes, thecombination of dyes providing two or more distinct detectable lightabsorbance spectral features,

a known volume of diluent solution that contains no dye, but which maycontain a buffer to maintain constant pH,

provision for the sample solution and the diluent solution to be mixed,either automatically or manually,

and computer executable firmware for calculating the volume of liquiddispensed by the dispenser being tested, based on the measurement ofabsorbance, the optical properties of the solutions, the dimensions ofthe vessel containing the mixture of sample and diluent solutions, andthe volume of diluent.

It is further to be noted that the present invention includes a systemfor testing or calibrating liquid delivery volume comprising at least aportion of the following:

a photometric measurement means that measures optical absorbance at morethan one wavelength and is capable of communicating results to anexternal printer or computer.

one or more sample solutions that are delivered by the device beingtested, each sample solution containing one or more dyes, thecombination of dyes providing two or more distinct detectable lightabsorbance spectral features,

a diluent solution that contains one or more dyes and which may containa buffer to maintain constant pH,

provision for the sample solution and the diluent solution to be mixed,either automatically or manually,

and computer executable firmware for calculating the volume of liquiddispensed by the dispenser being tested, based on the measurement ofabsorbance, the optical properties of the solutions, the dimensions ofthe vessel containing the mixture of sample and diluent solutions, andthe volume of diluent.

Other variations of the examples and designs described and shown hereincan be implemented. For example, and without intention to limit, adilution mode algorithm may be included to calculate volume based on thedilution of a dye. Additionally, the processes, steps thereof andvarious examples and variations of these processes and steps,individually or in combination, may be implemented as a computer programproduct tangibly embodied as computer-readable signals on acomputer-readable medium, for example, a non-volatile recording medium,an integrated circuit memory element, or a combination thereof. Such acomputer program product may include computer-readable signals tangiblyembodied on the computer-readable medium, where such signals defineinstructions, for example, as part of one or more programs that, as aresult of being executed by a computer, instruct the computer to performone or more processes or acts described herein, and/or various examples,variations and combinations thereof. Such instructions may be written inany of a plurality of programming languages, for example, Java, VisualBASIC, XML, C, or C++, Fortran, Pascal, Eiffel, BASIC, COBOL, and thelike, or any of a variety of combinations thereof.

It is to be understood that various modifications may be made to theapparatus, the method, and/or the kit as described herein withoutdeparting from the spirit and scope of the invention. For example,alternative dyes may be employed in a multi-dye solution. Accordingly,other embodiments are within the scope of the claims appended hereto.

What is claimed is:
 1. A method of determining a liquid volume of asample, the method comprising the steps of: a. providing in the sample asingle solution including one or more dyes selected to produce in thesample multiple distinct detectable light absorbance spectral features,wherein the one or more dyes establish in the solution a first distinctdetectable light absorbance spectral feature for a low volume ordilution range and a second distinct detectable light absorbancespectral feature for a high volume or dilution range; b. measuring thelight absorbance of multiple spectral features in the solution; and c.determining the volume of the sample from the measured light absorbanceof the sample.
 2. The method of claim 1 wherein the multiple distinctdetectable light absorbance spectral features are selected formeasurement where there is a valley or plateau resulting in a slopeclose to zero.
 3. The method of claim 1 comprising the step of selectingfor the solution a first dye and a second dye, wherein the first dyeestablishes in the solution the first distinct detectable lightabsorbance spectral feature for the low volume or dilution range and thesecond dye establishes the second distinct detectable light absorbancespectral feature for the high volume or dilution range.
 4. The method ofclaim 3 wherein the first dye is at a concentration giving a highabsorbance per unit pathlength in the solution and the second dye is ata concentration giving a low absorbance per unit pathlength in thesolution.
 5. The method of claim 1 comprising the step of selecting forthe solution a first dye and a second dye, wherein the first dyeestablishes in the solution the first distinct detectable lightabsorbance spectral feature for the first volume or dilution range andthe second distinct detectable light absorbance spectral feature for thesecond volume or dilution range, and the second dye establishes a thirddistinct detectable light absorbance spectral feature for a third volumeor dilution range and a fourth distinct detectable light absorbancespectral feature for a fourth volume or dilution range.
 6. The method ofclaim 1 comprising the step of selecting for the solution only one dyeto establish in the solution the first distinct detectable lightabsorbance spectral feature for the low volume or dilution range and thesecond distinct detectable light absorbance spectral feature for thehigh volume or dilution range.
 7. The method of claim 1 comprising thestep of selecting for the solution a first dye, a second dye, a thirddye and a fourth dye, wherein the first dye establishes in the solutionthe first distinct detectable light absorbance spectral feature for thelow volume or dilution range, the second dye establishes in the solutionthe second distinct detectable light absorbance spectral feature for thehigh volume or dilution range, the third dye establishes in the solutiona third distinct detectable light absorbance spectral feature for athird volume or dilution range, and the fourth dye establishes in thesolution a fourth distinct detectable light absorbance spectral featurefor a fourth volume or dilution range.